Quant Boosters  Hemant Malhotra  Set 6

(a + b)^2  (a^2 + b^2) = 2 * (ab)
(a + b + c)^2  (a^2 + b^2 + c^2) = 2 * (ab + bc + ca)
and so on
(1 + 2 + 3.........12)^2  (1^2 + 2^2......12^2) = 2 * (required answer)
so required value=5434/2=2717

Q26) There are three runners viz , Nishant , Deepak and Mohit who jog on the same path. Nishant goes jogging every two days. Deepak goes jogging every four days. Mohit goes jogging every seven days. If its the first day that they started this routine, what is the total number of days that each person will jog by himself in the next seven weeks?
(a) 12
(b) 13
(c) 14
(d) 15
(e) 16

Nishant = 25 days,
Deepak = 13 days,
Mohit = 7 days.
Nishant jogs on days 1,3,5,7,.....49, and Deepak jobs on days 1,5,9,.....49, and Mohit jogs on days 1, 8, 15, 22,...43.
when Deepak jogs, Nishant will always be jogging also, so Deepak jogs 0 days alone.
Nishant jogs 2513=12 days without Deepak also jogging,
but Mohit jogs on 4 odd numbered days, 2 of which Deepak also jogs, giving us 124+2=10 days that Nishant jogs alone.
Nishant jogs on every odd numbered day, so Mohit jogs alone only on even numbered days.
Because there are 4 odd numbered days , there are 3 even numbered days, so Mohit jogs alone on 3 days.
so
Nishant: 10
Deepak: 0
Mohit: 3
so 10+0+3=13

Q27) The sum of all the possible values of integral a such that (a^22a)^(a^2+47) = (a^22a)^(16a16) is
(a) 16
(b) 17
(c) 18
(d) 19
(e) none

a^2  2a will be equal to 0 or 1 or 1 then it’s possible
when a^2  2a = 0
so a=0,2
when a^22a=1 then not real values
a^22a=1 so a=1
so 0,1,2 these three possible values
now when same base
((a^2+47)= (16a16))
so a^216a+63=0
so a=7,9
so sum 0+1+2+7+9=19

Q28) Ten liters content of a milk water solution, which contain milk and water in the ratio 7:3 are removed and replaced with water to bring down the concentration of milk by 10% points. The amount (in liters) of water that needs to be added to the resulting solution in order to reduce the concentration of milk to 50% is?

When water= 7 liter extra
milk =7 liter decrease
then decrement of milk =10%
x * 10/100=7 so x=70 so total solution=70
now initially there was 49 liter milk and 21 liter water
but 7 liter milk reduced so 42 milk and 21+7=28 liter water
so (28+a)=(70+a) * 50% so a=14
If a and b are two real numbers such that a + b = 1, then find the maximum possible value of the product of (a^a x b^b) and (a^b and b^a)
a^(a+b) * b^(a+b)
a * b
if a+b=1 and we want max a * b so 1/4

Q29) Let {Vn} be a sequence such that V1 = 2, V2 = 1 and 2 Vn – 3 Vn1 + Vn–2 = 0 for n > 2, then find the value of V9.

V1=2
V2=1
2Vn3Vn1+Vn2=0 for n > 2
now put n=3
so 2V33V2+V1=0
so 2V3=3V2V1
so 2V3=32=1 so V3=1/2
now put n=4
2V43V3+V2=0
2V4=3 * 1/2 1=1/2 so V4=1/4
now check V1=2,V2=1,V3=1/2,V4=1/4 and So on so this is GP

Q30) sherlock homes and dr. watson have to travel from rajiv gandhi chowk to indira gandhi international airpot via the metro. they have enough coins of 1,5,10,25 paise. sherlock homes agrees to pay for dr. watson, only if he tells all the possible combination of coins that can be used to pay for the ticket. How many combinations are possible, if the fare is 50 paise?
a) 52
b) 49
c) 45
d) 44

a + 5b + 10c + 25d = 50 ,
Put d = 0, a + 5b + 10c = 50 now solve this
Put d = 1 then d = 2